Greetings from Denmark. As an EE I once had a MEMS course together with a group of physics students. During the lectures on simple electronics I was stumped at how little they actually knew about electrical networks. Filters were way out of their league, and we are talking about master students in their final year. So to identify a true EE I would simly ask for the expression for the 3dB frequency of a simple RC filter. That is something that every EE knows, no matter the specialisation.

Consider asking a EE what the effect on a resistor that temperature has or on a transistor. I do wonder how many EE grads have grounding in the basic physics of the devices. What is the effect on CMOS devices of temp/voltage?

My standard analog test is a zener shunt regulator. A few can correctly solve for the ballast resistor, but how much more they can say about what is going on is very revealing.
As a simple embodiment of non-linear resistance behaviour in a practical circuit it takes some beating.
They tell me they never looked at a zener in the same way again.
Next I would ask an candidate to explain what is actually going on in an inductor, and why we should care.
More mechanically, it is always fun to ask how the energy is stored in a spinning flywheel.
The better their maths, the harder it is to get the simple answer.

My thought process would be: 'This looks like a fuse, of course, but it might be a recent development in the field and they want to know if I am up-to-date. So I would look at it.'
Engineers specifically do not think like con-men when dealing with people. They do, however, specifically learn not to be naive about trusting stuff that has been made by people. the physical world. In this case I would question my knowledge being current (it ages several times faster than I do). Being trusting with people or taking things literally, are characteristics of engineers (for better or worse) and testing for them isn't a negative.
I also suspect I might look at the fuse anyway as I was thinking, simply because I always would look at something given to me in a test.

1. The fuse test - A long time ago we used to give rercuits a 20mm glas fuse and ask them which end was the positive and which negative. If the recruit looked to see if it was marked, he failed (you'd be suprised how many...)
2. Draw a wiring diagram of a stairway light that can be switched on or off at either end of the stairway (you'd be suprised how many can't...)

Correct PatrickYO, I was looking for the candidates understanding of "settling time"; nothing to do with Nyquist rates... The aim is to tease out the candidates practical understanding of how signals can be acquired accurately, and many engineers simply do not understand the basics - that signals have impedance, that capacitors need time to charge/discharge, and that careful attention to analog signal paths (and a host of other practical issues!) is required before even a 16bit ADCs can be used to its full accuracy with any confidence, let alone these 24-bit wonders...!
For a 10bit ADC, the least sig bit represents 1x10E-03 (actually, 1/1024) of the FSD of the signal. So, the voltage on the 100pF cap must get to 0.999 of its final value. Some basic math shows that this requires a time of about 7 taus (RC time constants), which is 7 x 100ns in this case.
Perhaps one can argue that knowing that a 10bit DAC needs 7 taus of setting time is a bit specialised; I mean, that number is very specific to 10-bit DACs, of course. However, 10-bit ADCs are very common, and I would expect an engineer involved in any form of signal interfacing to know this to within +/- 1 tau.